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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 506, Pages 83–88
DOI: https://doi.org/10.31857/S2686954322050186 (Mi danma303) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Limiting characteristics of queueing systems with vanishing perturbations

A. I. Zeifmanabc, V. Yu. Korolevade, R. V. Razumchika, Ya. A. Satinb, I. A. Kovalevbd

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
b Vologda State University, Vologda, Russia
c Vologda Research Center of the Russian Academy of Sciences, Vologda, Russia
d Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia
e Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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DOI: https://doi.org/10.31857/S2686954322050186
Abstract: We consider inhomogeneous continuous-time Markov chains with vanishing perturbations. It is proved that, under some natural conditions, the limiting regimes of the initial and perturbed chains coincide. We obtain explicit estimates, which allow construction of the limiting regime of the perturbed chain, and show how these results can be used in the analysis of several known classes of queuing systems.
Keywords: queuing systems, stability, vanishing perturbations.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 075-15-2020-799
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 075-15-2020-799.
Presented: I. A. Sokolov
Received: 20.01.2022
Revised: 23.05.2022
Accepted: 01.07.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 2, Pages 375–379
DOI: https://doi.org/10.1134/S1064562422050209
Bibliographic databases:
Document Type: Article
UDC: 519.217
Language: Russian
Citation: A. I. Zeifman, V. Yu. Korolev, R. V. Razumchik, Ya. A. Satin, I. A. Kovalev, “Limiting characteristics of queueing systems with vanishing perturbations”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 83–88; Dokl. Math., 106:2 (2022), 375–379
Citation in format AMSBIB
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\paper Limiting characteristics of queueing systems with vanishing perturbations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 506
\pages 83--88
\mathnet{http://mi.mathnet.ru/danma303}
\crossref{https://doi.org/10.31857/S2686954322050186}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531989}
\elib{https://elibrary.ru/item.asp?id=49787607}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 2
\pages 375--379
\crossref{https://doi.org/10.1134/S1064562422050209}
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